因数 (1/((a+h)^2)-1/(a^2))/h

解

因数

\frac{\frac{1}{( a + h ) ^{2}} - \frac{1}{a ^{2}}}{h}

- \frac{h + 2 a}{a ^{2} ( h + a ) ^{2}}

解答ステップ

\frac{\frac{1}{( a + h ) ^{2}} - \frac{1}{a ^{2}}}{h}

結合

\frac{1}{( a + h ) ^{2}} - \frac{1}{a ^{2}} : \frac{- h ( h + 2 a )}{a ^{2} ( h + a ) ^{2}}

= \frac{\frac{- h ( h + 2 a )}{a ^{2} ( h + a ) ^{2}}}{h}

分数の規則を適用する:

\frac{- a}{b} = - \frac{a}{b}

= \frac{- \frac{h ( h + 2 a )}{a ^{2} ( h + a ) ^{2}}}{h}

分数の規則を適用する:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{\frac{h ( h + 2 a )}{a ^{2} ( h + a ) ^{2}}}{h}

分数の規則を適用する:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

\frac{\frac{h ( h + 2 a )}{a ^{2} ( h + a ) ^{2}}}{h} = \frac{h ( h + 2 a )}{a ^{2} ( h + a ) ^{2} h}

= - \frac{h ( h + 2 a )}{a ^{2} ( h + a ) ^{2} h}

共通因数を約分する:

h

= - \frac{h + 2 a}{a ^{2} ( h + a ) ^{2}}